I think it's the exhaust. It started off with a leak in the flex pipe. After driving home one day I was making a U-Turn in front of my house and when I began to turn the wheel the other way to reverse the car shut off. It kept doing that each time I started it and then the battery eventually died (weak battery.) I jumped the car and drove it into the parking spot quickly.

Now when I jump start the car it would start, weakly idle and slowly the rpm meter would go lower and lower until the car just stops. And If I try and rev the car to keep it idled, put it into drive and turn the wheel the car would shut off. The car is real loud where the leak in the flex pipe is too.

I ordered brand new headers, flex pipe, and a whole catback exhaust last week and they'll be here tomorrow. I'm also going to get a new battery. What do you guys think? It's the exhaust right? Once I get these parts installed this problem should be fine right?

I took it down the street to the mechanic and he called me the next day and said one of my fuel injectors isn't working. He said that's why the car was running so hard, it was as if it was only running on 3 cylinders. Would this cause the problems I mentioned to happen?

A clogged/faulty injector would definitely cause that problem. I would recommend a new factory Nissan fuel filter and running a can of BG 44K and a tank of premium since they replaced one of your injectors.